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Volume 7, Number 4, 2017, Pages 1652-1673                                                                DOI:10.11948/2017101
Stability of a stochastic SEIS model with saturation incidence and latent period
Xuehui Ji,Sanling Yuan,Jiao Li
Keywords:Stochastic SEIS model, time delay, Lyapunov functional, It\^{o}'s formula, stochastic stability.
      In this paper, a stochastic SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. The model inherits the endemic steady state from its corresponding deterministic counterpart. We first show the existence and uniqueness of the global positive solution of the model. Then, by constructing Lyapunov functionals, we derive sufficient conditions ensuring the stochastic stability of the endemic steady state. Numerical simulations are carried out to confirm our analytical results. Furthermore, our simulation results shows that the existence of noise and delay may cause the endemic steady state to be unstable.
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